Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model

Abstract

Within the recently introduced auxiliary master equation approach it is possible to address steady state properties of strongly correlated impurity models, small molecules or clusters efficiently and with high accuracy. It is particularly suited for dynamical mean field theory in the nonequilibrium as well as in the equilibrium case. The method is based on the solution of an auxiliary open quantum system, which can be made quickly equivalent to the original impurity problem. In its first implementation a Krylov space method was employed. Here, we aim at extending the capabilities of the approach by adopting matrix product states for the solution of the corresponding auxiliary quantum master equation. This allows for a drastic increase in accuracy and permits us to access the Kondo regime for large values of the interaction. In particular, we investigate the nonequilibrium steady state of a single impurity Anderson model and focus on the spectral properties for temperatures T below the Kondo temperature TK and for small bias voltages φ. For the two cases considered, with T ≈ TK/4 and T ≈ TK/10 we find a clear splitting of the Kondo resonance into a two-peak structure for φ close above TK. In the equilibrium case (φ = 0) and for T ≈ TK/4, the obtained spectral function essentially coincides with the one from numerical renormalization group.

Thermoelectric response of a correlated impurity in the nonequilibrium Kondo regime

“…In contrast to the particle-hole symmetric case (s. Ref. 39) the splitting is asymmetric in presence of a finite gate voltage. According to Eq.…”

“…38,68 and in its recent MPS implementation Ref. 39. The basic principle of the approach is to map the original nonequilibrium (or equilibrium) impurity problem onto an auxiliary one, in which the bath is modeled by a small number N B of bath sites and additional Markovian environments.…”

“…39 For the calculation of thermoelectric properties one needs to consider systems away from particle-hole symmetry. In our previous calculations in Ref.…”

“…We use the recent implementation of the auxiliary master equation approach (AMEA) 38,[68][69][70] within matrix product states (MPS) 39 , which allows for a significantly improved accuracy as compared to previous implementations based on exact diagonalization 38,68 . The equilibrium results for the strongly interacting SIAM were benchmarked against NRG data, showing a remarkable agreement.…”

Efficient DMFT impurity solver using real-time dynamics with matrix product states

“…This suggests that these features are a generic property also of multi-orbital Hubbard models close to metalto Mott-insulator phase transitions. We note that this method is also well suited for applications within nonequilibrium DMFT 67 and non-equilibrium master equation approaches 68 . We tested the validity and precision of our method as an impurity solver for the case of the single impurity Anderson model at parameters for which results are available from the most precise technique to date, namely the dynamical DMRG 35,38,39,45 .…”